Characterizing susceptibility of a machine-learning model to follow signal degradation and evaluating possible mitigation strategies

ABSTRACT

The disclosed embodiments relate to a system that characterizes susceptibility of an inferential model to follow signal degradation. During operation, the system receives a set of time-series signals associated with sensors in a monitored system during normal fault-free operation. Next, the system trains the inferential model using the set of time-series signals. The system then characterizes susceptibility of the inferential model to follow signal degradation. During this process, the system adds degradation to a signal in the set of time-series signals to produce a degraded signal. Next, the system uses the inferential model to perform prognostic-surveillance operations on the set of time-series signals with the degraded signal. Finally, the system characterizes susceptibility of the inferential model to follow degradation in the signal based on results of the prognostic-surveillance operations.

BACKGROUND Field

The disclosed embodiments generally relate to techniques for usingmachine-learning (ML) models to perform prognostic-surveillanceoperations based on time-series sensor signals. More specifically, thedisclosed embodiments relate to a technique for characterizing thesusceptibility of an ML model to follow signal degradation andevaluating possible mitigation strategies.

Related Art

Large numbers of sensors are presently deployed to monitor theoperational health of critical assets in a large variety ofbusiness-critical systems. For example, a medium-sized computer datacenter can include over 1,000,000 sensors monitoring thousands ofservers, a modern passenger jet can include 75,000 sensors, an oilrefinery can include over 1,000,000 sensors, and even an ordinary carcan have over 100 sensors. These sensors produce large volumes oftime-series sensor data, which can be used to performprognostic-surveillance operations to facilitate detecting incipientanomalies. This makes it possible to take remedial action before theincipient anomalies develop into failures in the critical assets.

Machine-learning (ML) techniques are commonly used to performprognostic-surveillance operations on time-series sensor data, and alsofor validating the integrity of the sensors themselves. ML-basedprognostic-surveillance techniques typically operate by training an MLmodel (also referred to as an “inferential model”) to learn correlationsamong time-series signals. The trained ML model is then placed in asurveillance mode where it is used to predict values for time-seriessignals based on the correlations with other time-series signals,wherein deviations between actual and predicted values for thetime-series signals trigger alarms that indicate an incipient anomaly.This makes it possible to perform remedial actions before the underlyingcause of the incipient anomaly leads to a catastrophic failure.

However, because of the complex interplay of dependencies amongtime-series signals, smaller ML models with poor signal-to-noise ratiosoften generate predicted values that “follow” degradation in a signal.This is problematic because anomalies are normally discovered byprognostic-surveillance systems when a real signal deviates from themodel's predicted values. Hence, if the model's predicted values“follow” the real measured signal, no degradation is detected, which canbe dangerous in safety-critical industries, and costly in industries forwhich undetected anomalies lead to catastrophic failures.

The “Following phenomenon” occurs because ML models typically operate byperforming training operations that generate “weights” associated withthe correlations among signals. However, when an ML model is trained onrandom signals, the ML model is designed with the implicit understandingthat it cannot predict the random signals, so the ML model will set itsweights to zero. Hence, when new observations are received during thesurveillance mode, the model has zero weights, and the best predictedvalues will be the observations themselves. This means that when an MLmodel is too small or noisy, the predicted values will tend to followthe observations, which causes the residuals to become small, and makesit difficult to detect signal deviations.

Note that the “Following phenomenon” has nothing to do with the qualityof the monitored components or the accuracy of the sensors. Hence, if anasset owner replaces components and/or sensors because of missed alarms,and then puts the asset back into service, the ML-basedprognostic-surveillance techniques will still be subject to Followingand will continue to miss alarms.

Hence, what is needed is a technique for effectively characterizing andmitigating the effects of signal Following in ML-basedprognostic-surveillance systems.

SUMMARY

The disclosed embodiments relate to a system that characterizessusceptibility of an inferential model to follow signal degradation.During operation, the system receives a set of time-series signalsassociated with sensors in a monitored system during normal fault-freeoperation. Next, the system trains the inferential model using the setof time-series signals. The system then characterizes susceptibility ofthe inferential model to follow signal degradation. During this process,the system adds degradation to a signal in the set of time-seriessignals to produce a degraded signal. Next, the system uses theinferential model to perform prognostic-surveillance operations on theset of time-series signals with the degraded signal. Finally, the systemcharacterizes susceptibility of the inferential model to followdegradation in the signal based on results of theprognostic-surveillance operations.

In some embodiments, the process of characterizing susceptibility isrepeated for all signals in the set of time-series signals.

In some embodiments, the training and characterizing operations arerepeated while adding different degradation amplitudes to the signal todetermine how the different degradation amplitudes affect susceptibilityof the inferential model to follow signal degradation.

In some embodiments, the training and characterizing operations arerepeated while using different numbers of training vectors for theinferential model to determine how different numbers of training vectorsaffect susceptibility of the inferential model to follow signaldegradation.

In some embodiments, the training and characterizing operations arerepeated while adding different amounts of noise to the set oftime-series signals to determine how different amounts of noise affectsusceptibility of the inferential model to follow signal degradation.

In some embodiments, the training and characterizing operations arerepeated while using different numbers of time-series signals from theset of time-series signals to determine how using different numbers oftime-series signals affects susceptibility of the inferential model tofollow signal degradation.

In some embodiments, the degradation that is added to the signal is aramp-shaped degradation, which causes a corresponding slope in residualsgenerated using the inferential model. In these embodiments,characterizing the susceptibility of the inferential model to followdegradation involves computing a Following metric (FM), whereinFM=1−[Ratio(slope of residuals/slope of ramp)].

In some embodiments, the system additionally reports results of thecharacterization to a user or developer of the inferential model.

In some embodiments, when the characterizing operation indicates thatthe inferential model is susceptible to Following signal degradation,the system automatically suggests one or more of the following based onresults of the characterization: changing a number of training vectorsused to train the inferential model; performing filtering operations toremove noise from signals monitored by the inferential model; andchanging a number of signals monitored by the inferential model.

In some embodiments, during a surveillance mode, the system: uses theinferential model to generate estimated values based on subsequentlyreceived time-series signals from the monitored system; performs apairwise differencing operation between actual values and the estimatedvalues for the subsequently received time-series signals to produceresiduals; and analyzes the residuals to detect the incipient anomaliesin the monitored system.

In some embodiments, detecting the incipient anomalies in the monitoredsystem comprises detecting an impending failure of the monitored system,or a malicious-intrusion event in the monitored system.

In some embodiments, the received set of time-series signals comprisessynthesized signals generated by a high-fidelity signal synthesizer,which generates simulations of actual signals produced by sensors in themonitored system during normal fault-free operation.

BRIEF DESCRIPTION OF THE FIGURES

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 illustrates an exemplary prognostic-surveillance system inaccordance with the disclosed embodiments.

FIG. 2 presents a flow chart illustrating a process for training aninferential model in accordance with the disclosed embodiments.

FIG. 3 presents a flow chart illustrating a process for using aninferential model to perform a prognostic-surveillance operation inaccordance with the disclosed embodiments.

FIG. 4A presents a graph illustrating MSET estimates and original dataduring signal degradation for a model with no Following in accordancewith the disclosed embodiments.

FIG. 4B presents a graph illustrating residuals and associated SPRTalarms during signal degradation for a model with no Following inaccordance with the disclosed embodiments.

FIG. 5A presents a graph illustrating MSET estimates and original dataduring signal degradation for a model with Following in accordance withthe disclosed embodiments.

FIG. 5B presents a graph illustrating residuals and associated SPRTalarms during signal degradation for a model with Following inaccordance with the disclosed embodiments.

FIG. 6A presents a flow chart illustrating a process for characterizingFollowing and the effect of various parameters on it in accordance withthe disclosed embodiments.

FIG. 6B presents a flow chart illustrating a process for performingtests to characterize Following for different degradation amplitudes inaccordance with the disclosed embodiments.

FIG. 7A presents a graph illustrating the effect of signal noise andnumber of signals on Following in accordance with the disclosedembodiments.

FIG. 7B presents a graph illustrating the effect of number of modelvectors and number of signals on Following in accordance with thedisclosed embodiments.

FIG. 7C presents a graph illustrating the effect of degradationamplitude and number of signals on Following in accordance with thedisclosed embodiments.

FIG. 7D presents a graph illustrating the effect of number of modelvectors and signal noise on Following in accordance with the disclosedembodiments.

FIG. 7E presents a graph illustrating the effect of degradationamplitude and signal noise on Following in accordance with the disclosedembodiments.

FIG. 7F presents a graph illustrating the effect of degradationamplitude and number of model vectors on Following in accordance withthe disclosed embodiments.

FIG. 8 presents a high-level flow chart illustrating a process forcharacterizing susceptibility of an inferential model to follow signaldegradation in accordance with the disclosed embodiments.

DETAILED DESCRIPTION

The following description is presented to enable any person skilled inthe art to make and use the present embodiments, and is provided in thecontext of a particular application and its requirements. Variousmodifications to the disclosed embodiments will be readily apparent tothose skilled in the art, and the general principles defined herein maybe applied to other embodiments and applications without departing fromthe spirit and scope of the present embodiments. Thus, the presentembodiments are not limited to the embodiments shown, but are to beaccorded the widest scope consistent with the principles and featuresdisclosed herein.

The data structures and code described in this detailed description aretypically stored on a computer-readable storage medium, which may be anydevice or medium that can store code and/or data for use by a computersystem. The computer-readable storage medium includes, but is notlimited to, volatile memory, non-volatile memory, magnetic and opticalstorage devices such as disk drives, magnetic tape, CDs (compact discs),DVDs (digital versatile discs or digital video discs), or other mediacapable of storing computer-readable media now known or later developed.

The methods and processes described in the detailed description sectioncan be embodied as code and/or data, which can be stored in acomputer-readable storage medium as described above. When a computersystem reads and executes the code and/or data stored on thecomputer-readable storage medium, the computer system performs themethods and processes embodied as data structures and code and storedwithin the computer-readable storage medium. Furthermore, the methodsand processes described below can be included in hardware modules. Forexample, the hardware modules can include, but are not limited to,application-specific integrated circuit (ASIC) chips, field-programmablegate arrays (FPGAs), and other programmable-logic devices now known orlater developed. When the hardware modules are activated, the hardwaremodules perform the methods and processes included within the hardwaremodules.

Exemplary Prognostic-Surveillance System

Before describing techniques for characterizing susceptibility of aninferential model to follow signal degradation further, we firstdescribe an exemplary prognostic-surveillance system in which thetechniques can be used. FIG. 1 illustrates a prognostic-surveillancesystem 100 that accesses a time-series database 106, containingtime-series signals in accordance with the disclosed embodiments. Asillustrated in FIG. 1, prognostic-surveillance system 100 operates on aset of time-series sensor signals 104 obtained from sensors in amonitored system 102. Note that monitored system 102 can generallyinclude any type of machinery or facility, which includes sensors andgenerates time-series signals. Moreover, time-series signals 104 canoriginate from any type of sensor, which can be located in a componentin monitored system 102, including: a voltage sensor; a current sensor;a pressure sensor; a rotational speed sensor; and a vibration sensor.

During operation of prognostic-surveillance system 100, time-seriessignals 104 can feed into a time-series database 106, which stores thetime-series signals 104 for subsequent analysis. Next, the time-seriessignals 104 either feed directly from monitored system 102 or fromtime-series database 106 into a Multivariate State Estimation Technique(MSET) pattern-recognition model 108. Although it is advantageous to usean inferential model, such as MSET, for pattern-recognition purposes,the disclosed embodiments can generally use any one of a generic classof pattern-recognition techniques called nonlinear, nonparametric (NLNP)regression, which includes neural networks, support vector machines(SVMs), auto-associative kernel regression (AAKR), and even simplelinear regression (LR).

Next, MSET model 108 is “trained” to learn patterns of correlation amongall of the time-series signals 104. This training process involves aone-time, computationally intensive computation, which is performedoffline with accumulated data that contains no anomalies. Thepattern-recognition system is then placed into a “real-time surveillancemode,” wherein the trained MSET model 108 predicts what each signalshould be, based on other correlated variables; these are the “estimatedsignal values” 110 illustrated in FIG. 1. Next, the system uses adifference module 112 to perform a pairwise differencing operationbetween the actual signal values and the estimated signal values toproduce residuals 114. The system then performs a “detection operation”on the residuals 114 by using SPRT module 116 to detect anomalies andpossibly to generate an alarm 118. (For a description of the SPRT model,please see Wald, Abraham, June 1945, “Sequential Tests of StatisticalHypotheses.” Annals of Mathematical Statistics. 16 (2): 117-186.) Inthis way, prognostic-surveillance system 100 can proactively alertsystem operators of incipient anomalies, such as impending failures,hopefully with enough lead time so that such problems can be avoided orproactively fixed.

The prognostic surveillance system 100 illustrated in FIG. 1 operatesgenerally as follows. During a training mode, which is illustrated inthe flow chart in FIG. 2, the system receives a training set comprisingtime-series signals gathered from sensors in the monitored system undernormal fault-free operation (step 202). The system then trains theinferential model to predict values of the time-series signals based onthe training set (step 204). During a subsequent surveillance mode,which is illustrated by the flow chart in FIG. 3, the system receivesnew time-series signals gathered from sensors in the monitored system(step 302). Next, the system uses the inferential model to generateestimated values for the set of time-series signals based on the newtime-series signals (step 304). The system then performs a pairwisedifferencing operation between actual values and the estimated valuesfor the set of time-series signals to produce residuals (step 306). Thesystem then analyzes the residuals to detect the incipient anomalies inthe monitored system. This involves performing a SPRT on the residualsto produce SPRT alarms with associated tripping frequencies (step 308),and then detecting incipient anomalies based on the tripping frequencies(step 310). Note that these incipient anomalies can be associated withan impending failure of the monitored system, or a malicious-intrusionevent in the monitored system.

Following Metric

We have developed a new “Following metric” (FM) to facilitatecharacterizing the susceptibility of an ML model to follow signaldegradation. When an ML model is susceptible to Following, the modelestimates follow the degradation, so the residuals stabilize and/orremain close to zero, which means that anomaly are not discovered andsubsequently alerts are not generated. Conversely, when an ML model isnot susceptible to Following, when a signal drifts out of correlationwith other monitored signals, the residuals depart from zero, whichtriggers anomaly alerts. The above observations have guided us indeveloping a quantitative metric for characterizing the degree ofFollowing for any ML model that operates on any dataset of monitoredsignals.

Our Following metric (FM) ranges from zero to one, with higher valuesindicating that an ML model is susceptible to Following, and lowervalues indicating there is little susceptibility to Following. Thismetric is measured by introducing a ramp-shaped degradation into asignal and then measuring a resulting change in the slope of theresiduals.

More specifically, the Following metric FM is defined as follows.

FM=1−[ratio(slope of residuals/slope of ramp)]

Hence, if a ramp-shaped degradation in a signal does not cause acorresponding slope in the residuals, this means that the ML model is“Following” the degradation. This means the ratio (slope ofresiduals/slope of ramp) is zero and the FM=1. Conversely, if theramp-shaped degradation causes a similar slope in the residuals, thismeans that the inferential model is “not Following” the degradation, sothe ratio (slope of residuals/slope of ramp)≈1 and the FM≈0.

Exemplary Use Case

We now present results for an exemplary use case, which can possiblyarise in utility system asset prognostics as well as in prognostics forservers in computer data centers. In this example, each signal has10,000 time-series observations without any degradation. We use ananalytical fault simulator to introduce a ramp-shaped degradation inSignal 5 starting from observation number 7,501 as illustrated in FIGS.4A, 4B, 5A and 5B. Note that this ramp-shaped degradation simulates acommon degradation mode for physical sensors, which is referred to as“linear de-calibration bias.” In this example, the collection of signalsis fit to an MSET model and the residuals (differences between actualsignal values and MSET estimates) are passed through a SPRT to detectdegradation and generate corresponding SPRT alarms.

When the MSET model is not subject to signal Following, thecorresponding residuals will cause SPRT alarms to be generated as isillustrated in FIGS. 4A-4B. More specifically, FIG. 4A presents a graphillustrating an original data signal (in red), which is overlaid on acorresponding MSET estimate signal (in blue). Note that the originaldata signal ramps up, but the estimated signal does not because theestimated signal reflects what the original data is supposed to be (ifthere were no degradation). The top graph in FIG. 4B illustrates how theresulting residual signal ramps up from observation 7,501 to observation10,000. This ramp causes a corresponding increase in SPRT alarms as isillustrated in the bottom graph in FIG. 4B.

In contrast, when the MSET model is subject to signal Following, thecorresponding residuals will not cause SPRT alarms as is illustrated inFIGS. 5A-5B. More specifically, FIG. 5A presents a graph illustrating anoriginal data signal (in red), which is overlaid on a corresponding MSETestimate signal (in blue). Note that the original data signal ramps up,which is caused by the simulated degradations, yet the estimate signal“follows” the original data signal and also ramps up, so the two signalsessentially match. The top graph in FIG. 5B illustrates how theresulting residual signal only ramps up slightly from observation 7,501up to observation 10,000. This slight ramp in residuals is statisticallyinsufficient to cause SPRT alarms to be generated as is illustrated inthe bottom graph in FIG. 5B.

Characterizing Following

To better understand the Following phenomena and the effect of variousparameters on it, we conducted an investigation that performed aparametric sweep across a number of parameters for an exemplary systemto determine how the parameters influence the degree of Following. Theseparameters include: (1) number of signals used by the MSET model(NumSigs), (2) signal noise measures with respect to a standarddeviation (STD), (3) number of training vectors for the MSET model(NumVecs), and (4) amplitude of the ramp-shaped degradation (DegRamp).

A flow chart for this parametric sweep appears in FIGS. 6A-6B. The flowchart in FIG. 6A includes three nested loops involving steps 602 through620 that cycle through all possible values for NumSigs, STD and NumVecs.At the core of these nested loops, an MSET model is trained (step 608)and tests are performed to determine a degree of Following for differentdegradation amplitudes (step 610). Finally, the system reports FMmetrics (step 624).

The flow chart in FIG. 6B illustrates operations that take place in step610 of the flow chart in FIG. 6A. In FIG. 6B, a loop, which isimplemented by steps 632, 640 and 642, cycles through all possibleamplitudes of ramp degradation. Within this loop, the system executesthe MSET model (step 634) to generate estimates and correspondingresiduals that feed into a SPRT module (step 636). The system alsocalculates and stores an FM (step 638).

The above-described comprehensive parametric analysis ensures for anyset of monitored signals (per a customer's use case) that the systemdetermines whether the inferential model is absolutely robust (with nopossibility of Following). Otherwise, if Following is detected, an alertis sent to a data scientist indicating that the model is susceptible toFollowing. At this point, a mitigation analysis can be performed todetermine optimal values of the parameters to minimize Following. (Notethat, in some use cases, optimal parameters can mitigate or eliminatethe Following phenomenon. However, in other use cases, the Followingphenomenon cannot be eliminated by adjusting the parameters.)

The mitigation analysis can be facilitated by generating graphs, whichillustrate how the Following metric varies for various combinations ofparameters. In particular, FIG. 7A illustrates the effect of signalnoise and number of signals on Following while NumVecs is fixed at 100and DegRamp is fixed at 2.5. FIG. 7B presents a graph illustrating theeffect of number of model vectors and number of signals on Followingwhile STD is fixed at 1 and DegRamp is fixed at 2.5. FIG. 7C illustratesthe effect of degradation amplitude and number of signals on Followingwhile STD is fixed at 1 and NumVecs is fixed at 100. FIG. 7D illustratesthe effect of number of model vectors and signal noise on Followingwhile NumSigs is fixed at 40 and DegRamp is fixed at 2.5. FIG. 7Eillustrates the effect of degradation amplitude and signal noise onFollowing while NumSigs is fixed at 40 and NumVecs is fixed at 100. FIG.7F illustrates the effect of degradation amplitude and number of modelvectors on Following while NumSigs is fixed at 40 and STD is fixed at 1.Note that the graphs illustrated in FIGS. 7A-7F provide sufficientinformation to determine the optimal combination of parameters tominimize Following.

High-Level Process for Characterizing Following

FIG. 8 presents a high-level flow chart illustrating a process forcharacterizing susceptibility of an inferential model to follow signaldegradation Following in accordance with the disclosed embodiments.During operation, the system receives a set of time-series signalsassociated with sensors in a monitored system during normal fault-freeoperation (step 802). Next, the system trains the inferential modelusing the set of time-series signals (step 804). The system thencharacterizes susceptibility of the inferential model to follow signaldegradation. During this process, the system adds degradation to asignal in the set of time-series signals to produce a degraded signal(step 806). Next, the system uses the inferential model to performprognostic-surveillance operations on the set of time-series signalswith the degraded signal (step 808). The system then characterizessusceptibility of the inferential model to follow degradation in thesignal based on results of the prognostic-surveillance operations (step810). Note that the process for characterizing susceptibility performedin steps 806, 808 and 810 is repeated for all signals in the set oftime-series signals. Also, note that the training and characterizingoperations performed in steps 804 806, 808 and 810 is repeated for:different degradation amplitudes; different amounts of noise; anddifferent numbers of signals and training vectors Finally, when thecharacterizing operation indicates that the inferential model issusceptible to Following signal degradation, the system suggests one ormore of the following: changing a number of training vectors used totrain the inferential model; performing filtering operations to removenoise from signals monitored by the inferential model; and changing anumber of signals monitored by the inferential model (step 812).

Various modifications to the disclosed embodiments will be readilyapparent to those skilled in the art, and the general principles definedherein may be applied to other embodiments and applications withoutdeparting from the spirit and scope of the present invention. Thus, thepresent invention is not limited to the embodiments shown, but is to beaccorded the widest scope consistent with the principles and featuresdisclosed herein.

The foregoing descriptions of embodiments have been presented forpurposes of illustration and description only. They are not intended tobe exhaustive or to limit the present description to the formsdisclosed. Accordingly, many modifications and variations will beapparent to practitioners skilled in the art. Additionally, the abovedisclosure is not intended to limit the present description. The scopeof the present description is defined by the appended claims.

What is claimed is:
 1. A method for characterizing susceptibility of aninferential model to follow signal degradation, comprising: receiving aset of time-series signals associated with sensors in a monitored systemduring normal fault-free operation; training the inferential model usingthe set of time-series signals; and characterizing susceptibility of theinferential model to follow signal degradation by, adding degradation toa signal in the set of time-series signals to produce a degraded signal,using the inferential model to perform prognostic-surveillanceoperations on the set of time-series signals with the degraded signal,and characterizing the susceptibility of the inferential model to followdegradation in the signal based on results of theprognostic-surveillance operations.
 2. The method of claim 1, whereinthe process of characterizing susceptibility is repeated for all signalsin the set of time-series signals.
 3. The method of claim 1, wherein thetraining and characterizing operations are repeated while addingdifferent degradation amplitudes to the signal to determine how thedifferent degradation amplitudes affect susceptibility of theinferential model to follow signal degradation.
 4. The method of claim1, wherein the training and characterizing operations are repeated whileusing different numbers of training vectors for the inferential model todetermine how different numbers of training vectors affectsusceptibility of the inferential model to follow signal degradation. 5.The method of claim 1, wherein the training and characterizingoperations are repeated while adding different amounts of noise to theset of time-series signals to determine how different amounts of noiseaffect susceptibility of the inferential model to follow signaldegradation.
 6. The method of claim 1, wherein the training andcharacterizing operations are repeated while using different numbers oftime-series signals from the set of time-series signals to determine howusing different numbers of time-series signals affects susceptibility ofthe inferential model to follow signal degradation.
 7. The method ofclaim 1, wherein the degradation that is added to the signal is aramp-shaped degradation, which causes a corresponding slope in residualsgenerated using the inferential model; and wherein characterizing thesusceptibility of the inferential model to follow degradation involvescomputing a Following metric (FM), whereinFM=1−[Ratio(slope of residuals/slope of ramp)].
 8. The method of claim1, further comprising reporting results of the characterization to auser or developer of the inferential model.
 9. The method of claim 1,wherein when the characterizing operation indicates that the inferentialmodel is susceptible to Following signal degradation, the method furthercomprises automatically suggesting one or more of the following based onresults of the characterization: changing a number of training vectorsused to train the inferential model; performing filtering operations toremove noise from signals monitored by the inferential model; andchanging a number of signals monitored by the inferential model.
 10. Themethod of claim 1, wherein during a surveillance mode, the methodfurther comprises: using the inferential model to generate estimatedvalues based on subsequently received time-series signals from themonitored system; performing a pairwise differencing operation betweenactual values and the estimated values for the subsequently receivedtime-series signals to produce residuals; and analyzing the residuals todetect the incipient anomalies in the monitored system.
 11. The methodof claim 10, wherein detecting the incipient anomalies in the monitoredsystem comprises detecting one or more of the following: an impendingfailure of the monitored system; and a malicious-intrusion event in themonitored system.
 12. The method of claim 1, wherein the received set oftime-series signals comprises synthesized signals generated by ahigh-fidelity signal synthesizer, which generates simulations of actualsignals produced by sensors in the monitored system during normalfault-free operation.
 13. A non-transitory computer-readable storagemedium storing instructions that when executed by a computer cause thecomputer to perform a method for characterizing susceptibility of aninferential model to follow signal degradation, the method comprising:receiving a set of time-series signals associated with sensors in amonitored system during normal fault-free operation; training theinferential model using the set of time-series signals; andcharacterizing susceptibility of the inferential model to follow signaldegradation by, adding degradation to a signal in the set of time-seriessignals to produce a degraded signal, using the inferential model toperform prognostic-surveillance operations on the set of time-seriessignals with the degraded signal, and characterizing the susceptibilityof the inferential model to follow degradation in the signal based onresults of the prognostic-surveillance operations.
 14. Thenon-transitory computer-readable storage medium of claim 13, wherein theprocess of characterizing susceptibility is repeated for all signals inthe set of time-series signals.
 15. The non-transitory computer-readablestorage medium of claim 13, wherein the training and characterizingoperations are repeated while adding different degradation amplitudes tothe signal to determine how the different degradation amplitudes affectsusceptibility of the inferential model to follow signal degradation.16. The non-transitory computer-readable storage medium of claim 13,wherein the training and characterizing operations are repeated while:using different numbers of training vectors for the inferential model todetermine how different numbers of training vectors affectsusceptibility of the inferential model to follow signal degradation;adding different amounts of noise to the set of time-series signals todetermine how different amounts of noise affect susceptibility of theinferential model to follow signal degradation; and using differentnumbers of time-series signals from the set of time-series signals todetermine how using different numbers of time-series signals affectssusceptibility of the inferential model to follow signal degradation.17. The method of claim 13, wherein the degradation that is added to thesignal is a ramp-shaped degradation, which causes a corresponding slopein residuals generated using the inferential model; and whereincharacterizing the susceptibility of the inferential model to followdegradation involves computing a Following metric (FM), whereinFM=1−[Ratio(slope of residuals/slope of ramp)].
 18. The non-transitorycomputer-readable storage medium of claim 13, wherein when thecharacterizing operation indicates that the inferential model issusceptible to Following signal degradation, the method furthercomprises automatically suggesting one or more of the following based onresults of the characterization: changing a number of training vectorsused to train the inferential model; performing filtering operations toremove noise from signals monitored by the inferential model; andchanging a number of signals monitored by the inferential model.
 19. Thenon-transitory computer-readable storage medium of claim 13, whereinduring a surveillance mode, the method further comprises: using theinferential model to generate estimated values based on subsequentlyreceived time-series signals from the monitored system; performing apairwise differencing operation between actual values and the estimatedvalues for the subsequently received time-series signals to produceresiduals; and analyzing the residuals to detect the incipient anomaliesin the monitored system.
 20. A system that characterizes susceptibilityof an inferential model to follow signal degradation, comprising: atleast one processor and at least one associated memory; and aprognostic-surveillance mechanism that executes on the at least oneprocessor, wherein during operation, the prognostic-surveillancemechanism: receives a set of time-series signals associated with sensorsin a monitored system during normal fault-free operation; trains theinferential model using the set of time-series signals; andcharacterizes susceptibility of the inferential model to follow signaldegradation, wherein during the characterization, theprognostic-surveillance mechanism, adds degradation to a signal in theset of time-series signals to produce a degraded signal, uses theinferential model to perform prognostic-surveillance operations on theset of time-series signals with the degraded signal, and characterizessusceptibility of the inferential model to follow degradation in thesignal based on results of the prognostic-surveillance operations.